Importing Libraries

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scikitplot.cluster import plot_elbow_curve
from scikitplot.decomposition import plot_pca_component_variance
from scikitplot.metrics import plot_silhouette
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
import plotly.express as px
from plotly.offline import init_notebook_mode,iplot
init_notebook_mode(connected=True) 

Parsing Data and Getting Metrics of Features

data = pd.read_csv("data.csv",index_col='id')
data

	f_00	f_01	f_02	f_03	f_04	f_05	f_06	f_07	f_08	f_09	...	f_19	f_20	f_21	f_22	f_23	f_24	f_25	f_26	f_27	f_28
id
0	-0.389420	-0.912791	0.648951	0.589045	-0.830817	0.733624	2.258560	2	13	14	...	-0.478412	-0.757002	-0.763635	-1.090369	1.142641	-0.884274	1.137896	1.309073	1.463002	0.813527
1	-0.689249	-0.453954	0.654175	0.995248	-1.653020	0.863810	-0.090651	2	3	6	...	-0.428791	-0.089908	-1.784204	-0.839474	0.459685	1.759412	-0.275422	-0.852168	0.562457	-2.680541
2	0.809079	0.324568	-1.170602	-0.624491	0.105448	0.783948	1.988301	5	11	5	...	-0.413534	-1.602377	1.190984	3.267116	-0.088322	-2.168635	-0.974989	1.335763	-1.110655	-3.630723
3	-0.500923	0.229049	0.264109	0.231520	0.415012	-1.221269	0.138850	6	2	13	...	0.619283	1.287801	0.532837	1.036631	-2.041828	1.440490	-1.900191	-0.630771	-0.050641	0.238333
4	-0.671268	-1.039533	-0.270155	-1.830264	-0.290108	-1.852809	0.781898	8	7	5	...	-1.628830	-0.434948	0.322505	0.284326	-2.438365	1.473930	-1.044684	1.602686	-0.405263	-1.987263
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
97995	0.237591	1.657034	-0.689282	0.313710	-0.299039	0.329139	1.607378	5	7	8	...	-0.290116	-0.258141	-0.973640	1.369508	0.391055	2.152426	-0.208944	-1.475403	0.298448	0.445039
97996	0.322696	0.710411	0.562625	-1.321713	-0.357708	0.182024	0.178558	3	9	2	...	0.117687	1.388242	0.342400	1.680537	-0.860409	0.579165	1.162692	0.134994	0.994666	0.727642
97997	-0.249364	-0.459545	1.886122	-1.340310	0.195029	-0.559520	-0.379767	8	9	10	...	-0.850223	-1.787648	-1.268115	-1.508330	1.945622	1.503645	0.194968	2.142693	1.646042	0.641466
97998	0.311408	2.185237	0.761367	0.436723	0.464967	0.062321	-0.334025	1	8	11	...	-0.010839	1.118906	1.565765	0.358480	0.547615	1.224439	-0.537998	-1.610954	-0.616227	-0.066211
97999	0.755170	0.567483	1.456767	-0.579071	-0.048474	-1.206240	0.784305	0	11	3	...	1.180805	-0.925705	-1.368680	-2.465425	1.453582	-1.685122	0.129689	-0.970897	1.404988	-0.711098

98000 rows × 29 columns

data.describe()

	f_00	f_01	f_02	f_03	f_04	f_05	f_06	f_07	f_08	f_09	...	f_19	f_20	f_21	f_22	f_23	f_24	f_25	f_26	f_27	f_28
count	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	...	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000	98000.000000
mean	0.001220	0.005580	-0.001042	-0.000700	-0.003522	-0.001612	-0.003042	5.545918	6.763061	8.193163	...	-0.004513	-0.000515	-0.001670	-0.038752	-0.220002	0.166434	-0.064309	-0.062540	0.098472	-0.230910
std	1.002801	1.000742	1.001373	1.000422	1.003061	1.000532	0.997434	3.691840	4.152348	5.904919	...	1.004372	1.002962	0.999703	1.477858	1.494836	1.543014	1.576086	1.428055	1.305407	1.528476
min	-4.732235	-4.202795	-4.377021	-4.010826	-4.535903	-4.300767	-4.894525	0.000000	0.000000	0.000000	...	-4.894525	-4.732235	-4.438130	-6.873999	-8.234305	-7.792363	-6.593842	-7.375719	-7.335556	-6.954151
25%	-0.675226	-0.670985	-0.672779	-0.672540	-0.682510	-0.675066	-0.680421	3.000000	4.000000	4.000000	...	-0.678773	-0.679777	-0.675147	-1.022964	-1.203204	-0.903385	-1.128966	-0.975680	-0.746489	-1.262606
50%	0.002022	0.006650	-0.000324	-0.003185	-0.003307	0.001024	-0.002053	5.000000	6.000000	7.000000	...	-0.000587	-0.000806	0.000819	-0.056687	-0.219046	0.167074	-0.099221	-0.070852	0.082230	-0.271319
75%	0.677271	0.677746	0.677086	0.672097	0.677589	0.673344	0.668112	8.000000	9.000000	11.000000	...	0.672149	0.675437	0.676881	0.930158	0.764690	1.217432	0.987684	0.843212	0.925306	0.770516
max	4.490521	4.324974	4.560247	4.399373	4.050549	4.710316	3.998595	32.000000	30.000000	44.000000	...	4.560247	4.399373	4.135419	6.517721	6.054831	7.527271	7.544731	7.005608	7.205971	6.977150

8 rows × 29 columns

Heatmap to show correlations between features

plt.figure(figsize=(40,30))
X=data[['f_00','f_01','f_02','f_03','f_04','f_05','f_06','f_07','f_08','f_09','f_10','f_11','f_12','f_13','f_14','f_15','f_16','f_17','f_18','f_19','f_20','f_21','f_22','f_23','f_24','f_25','f_26','f_27','f_28']]
sns.heatmap(X.corr(),annot=True)

<AxesSubplot:>

Values are standardized to simplify clustering process

scaler = StandardScaler()
X_std = scaler.fit_transform(X)
X_std

array([[-0.3895505 , -0.91769495,  0.649105  , ...,  0.96048158,
         1.04529612,  0.68332274],
       [-0.6885438 , -0.45919476,  0.65432122, ..., -0.55294213,
         0.3554352 , -1.60267076],
       [ 0.80560694,  0.31875345, -1.16796258, ...,  0.97917134,
        -0.92625017, -2.22432704],
       ...,
       [-0.24988501, -0.46478181,  1.88458578, ...,  1.54422962,
         1.1855134 ,  0.57075203],
       [ 0.30932332,  2.17805293,  0.7613671 , ..., -1.08428749,
        -0.5474945 ,  0.10775421],
       [ 0.75184799,  0.56149   ,  1.45581708, ..., -0.63608329,
         1.00085474, -0.31416284]])

Initial KMeans Model

model = KMeans(n_clusters=5)

Scikitplot module is used to plot SSE values and clustering durations from 1 to 11 clusters

plot_elbow_curve(model, X_std)

<AxesSubplot:title={'center':'Elbow Plot'}, xlabel='Number of clusters', ylabel='Sum of Squared Errors'>

SSE values are shown based on number of clusters in dataframe

sse = []
for n in range(1, 12):
    kmeans = KMeans(n_clusters=n)
    kmeans.fit(X_std)
    sse.append(kmeans.inertia_)

sse_data = pd.DataFrame()
sse_data['Number of Clusters'] = range(1,12)
sse_data['SSE'] = sse
sse_data

	Number of Clusters	SSE
0	1	2.842000e+06
1	2	2.727188e+06
2	3	2.650155e+06
3	4	2.591869e+06
4	5	2.546540e+06
5	6	2.515479e+06
6	7	2.490155e+06
7	8	2.467124e+06
8	9	2.448185e+06
9	10	2.431116e+06
10	11	2.415682e+06

PCA is used with six components to create silhouette plot through cluster labels

pca = PCA(n_components=6)
pca.fit(X)
X_pca=pca.transform(X)
X_pca

array([[ 1.55615749, -5.55761901, -3.27033444, -8.10451241,  0.07160189,
        -1.38545715],
       [-4.56847689,  0.73947323, 10.15778924, -2.02184815,  2.6929648 ,
        -0.60118678],
       [-4.35162356, -1.55351235, -3.40598442, -0.57164416, -5.90081356,
         1.27071841],
       ...,
       [ 3.22977612, -0.46293048, -2.8466608 ,  1.53698353, -1.34452581,
        -4.53622615],
       [ 3.00420965,  5.38436588,  1.90883229, -4.45553122, -1.48407363,
        -2.2999682 ],
       [-8.76284074,  0.40598569, -1.99838805, -7.08410411,  6.23535882,
         1.76794389]])

cluster_labels = model.fit_predict(X_std)
cluster_labels

array([2, 1, 2, ..., 3, 4, 2])

plot_silhouette(X_pca, cluster_labels)

<AxesSubplot:title={'center':'Silhouette Analysis'}, xlabel='Silhouette coefficient values', ylabel='Cluster label'>

Features 13 and 12 have the greatest correlation before standardization, and correlation between feature 8 and 11 had the second greatest correlation before standardization

Testing is done through 3D scatter plot showing all three features catagorized by number of clusters in fitted and predicted model

model.fit(X_std)
ykmeans = model.predict(X_std)
cluster_num=[]
for i in range(len(ykmeans)):
    cluster_num.append(ykmeans[i]+1)
fig = px.scatter_3d(x=X_std[:,13], y=X_std[:,12], z=X_std[:,8],
                    color=cluster_num,
                    labels={
                     "x": "Standardized Feature 13",
                     "y": "Standardized Feature 12",
                     "z": "Standardized Feature 8",
                     "color": "Number of Clusters"
                 })
fig.show()

cluster_num=[]
for i in range(len(ykmeans)):
    cluster_num.append(ykmeans[i]+1)
fig = px.scatter_3d(x=X_std[:,13], y=X_std[:,12], z=X_std[:,11],
                    color=cluster_num,
                    labels={
                     "x": "Standardized Feature 13",
                     "y": "Standardized Feature 12",
                     "z": "Standardized Feature 11",
                     "color": "Number of Clusters"
                 })
fig.show()